Bartlett, M. S. (1963). The spectral analysis of point processes. Journal of the Royal Statistical Society, Series B: Statistical Methodology, 25(2), 264–281.
Bobkov, S., & Ledoux, M. (2019). One-dimensional empirical measures, order statistics, and Kantorovich transport distances. Memoirs of the American Mathematical Society, 261(1259)
Brunel, N., & Hakim, V. (2008). Sparsely synchronized neuronal oscillations. Chaos: An Interdisciplinary Journal of Nonlinear Science, 18(1), 015113
Brunel, N., & Hakim, V. (1999). Fast global oscillations in networks of integrate-and-fire neurons with low firing rates. Neural Computation, 11(7), 1621–1671.
Article CAS PubMed Google Scholar
Buzsáki, G. (2006). Rhythms of the Brain. Oxford: Oxford UP.
Buzsáki, G., & Draguhn, A. (2004). Neuronal oscillations in cortical networks. Science, 304, 1926–1929.
Ciba, M., Isomura, T., Jimbo, Y., et al. (2018). Spike-contrast: A novel time scale independent and multivariate measure of spike train synchrony. Journal of Neuroscience Methods, 293, 136–143. https://doi.org/10.1016/j.jneumeth.2017.09.008
Del Barrio, E., Giné, E., & Matrán, C. (1999). Central limit theorems for the Wasserstein distance between the empirical and the true distributions. Annals of Probability 1009–1071
Ginzburg, I., & Sompolinsky, H. (1994). Theory of correlations in stochastic neural networks. Physical Review E, 50(4), 3171.
Golomb, D., Hansel, D., & Mato, G. (2001). Mechanisms of synchrony of neural activity in large networks. In F. Moss & S. Gielen (Eds.), Neuro-informatics and Neural Modeling, Handbook of Biological Physics (Vol. 4, pp. 887–968). NY: Elsevier.
Hansel, D., & Sompolinsky, H. (1996). Chaos and synchrony in a model of a hypercolumn in visual cortex. Journal of Computational Neuroscience, 3(1), 7–34.
Article CAS PubMed Google Scholar
Hindmarsh, J. L., & Rose, R. M. (1984). A model for neuronal bursting using three coupled first order differential equations. Proceeding of the Royal Society: London Series B, 221, 87–102.
Hodgkin, A., & Huxley, A. (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. The Journal of Physiology, 117, 500–544. https://doi.org/10.1113/jphysiol.1952.sp004764
Kantorovich, L. V., & Rubinshtein, S. G. (1958). On a space of totally additive functions. Vestnik of the St Petersburg University: Mathematics, 13(7), 52–59.
Ostojic, S., Brunel, N., & Hakim, V. (2009). Synchronization properties of networks of electrically coupled neurons in the presence of noise and heterogeneities. Journal of Computational Neuroscience, 26, 369–392.
Pikovsky, A., & Rosenblum, M. (2024). A unified quantification of synchrony in globally coupled populations with the Wiener order parameter. Chaos: An Interdisciplinary Journal of Nonlinear Science, 34(5). https://doi.org/10.1063/5.0203645
Pikovsky, A., Rosenblum, M., & Kurths, J. (1996). Synchronization in a population of globally coupled chaotic oscillators. Europhysics Letters, 34(3), 165–170.
Press, W. H., Teukolsky, S. T., Vetterling, W. T., et al. (1992). Numerical Recipes in C: the Art of Scientific Computing (2nd ed.). Cambridge, England: Cambridge University Press.
Pu, S., & Thomas, P. J. (2020). Fast and accurate Langevin simulations of stochastic Hodgkin-Huxley dynamics. Neural Computation, 32(10), 1775–1835.
Quian Quiroga, R., Reddy, L., & Kreiman, G. (2005). Invariant visual representation by single neurons in the human brain. Nature, 435, 1102–1107. https://doi.org/10.1038/nature03687
Singer, W. (1993). Synchronization of cortical activity and its putative role in information processing and learning. Annual Review of Physiology, 55, 349–374.
Article CAS PubMed Google Scholar
Singer, W. (1999). Neuronal synchrony: A versatile code for the definition of relations? Neuron, 24, 49–65. https://doi.org/10.1016/s0896-6273(00)80821-1
Article CAS PubMed Google Scholar
Telenczuk, B., Destexhe, A. (2022). Local field potential, relationship to unit activity. In Jaeger, D., & Jung, R. (Eds.), Encyclopedia of Computational Neuroscience (1865-1870), Springer, N.Y.
Vaserstein, L. N. (1969). Markov processes over denumerable products of spaces, describing large systems of automata. Problemy Peredachi Informatsii, 5(3), 64–72.
Wiener, N. (1930). Generalized harmonic analysis. Acta Mathematica, 55(1), 117–258.
Willett, F., Kunz, E., Fan, C., et al. (2023). A high-performance speech neuroprosthesis. Nature, 620, 1031–1036. https://doi.org/10.1038/s41586-023-06377-x
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